Vibrating beam transducers are frequently used in modern sensors to provide an electrical signal representative of the force applied to the sensor. Vibrating beam transducers may be formed out of piezoelectric material, material that, when a signal is applied, develops a stress, and, conversely, when a stress is applied to the material, a voltage develops on the surface of the material. A vibrating beam transducer has a resonant frequency at which cyclical stressing results in a peak admittance and a minimum impedance to signals applied to the transducer. In some vibrating beam transducers, the resonant frequency of the transducer changes in proportion to the force-induced stress to which the beam is subjected. Force-measuring sensors that employ vibrating beam transducers operate by applying a voltage to the transducer which is used to establish the resonant frequency of the transducer that, in turn, is measured as an indication of the force applied to the transducer. Vibrating beam transducers that measure force are frequently employed in sensors used to measure weight, pressure and acceleration, since each of these parameters can be measured as a function of applied force.
Most piezoelectric vibrating beam transducers are formed from crystalline quartz which has piezoelectric properties that are well suited to force measurement. A vibrating beam transducer is typically in the form of a double-ended tuning fork with two beams secured together at their ends by integral mounting pads. The beams of the tuning fork are the actual vibrating beams. Electrodes on the beams (or on at least one of the mounting pads) provide the necessary signal to excite the beams into resonant vibration. In the preferred operating mode of many vibrating transducers, when a signal is applied to the beams, the individual beams vibrate 180.degree. out of phase with each other. When the beams so vibrate, they are referred to as being mechanically in phase with each other in a common plane. When the beams vibrate in phase, the force and torque end reactions of one beam are cancelled by the equal and opposite reactions of the other beam, minimizing the energy transfer between the mounting surface and the transducer and the support structures to which it is attached.
In an ideal vibrating beam transducer, at the resonant frequency, no mechanical energy should be transmitted from the transducer to the support structure. The removal of energy at the resonant frequency of the transformer lowers the quality factor of the transducer which is a measure of the ability of the transducer to resonate at a precisely defined frequency. A transducer with a lower quality factor provides output signals that are less precise measurements of force applied to the transducer.
One cause of energy transfer in many vibrating beam transducers is that the beams do not have identical resonant frequencies. Different isolated resonant frequencies in the individual beams can be attributed to the slight, but inevitable, variations in individual tine shape and dimensions. Still another cause of some differences in resonant frequencies of the beams is asymmetry in the facets where the beams join the mounting pads are asymmetric which results in the tines having different bending stiffnesses. Consequently, because of these differences, the two individual beams, even though formed out of a single piece of quartz, often have slightly different separate, or isolated, natural resonant frequencies. Thus, when an oscillating voltage is applied to the beams, the resultant resonant frequency of the transducer as a whole is at an intermediate frequency between the isolated resonant frequencies of the individual beams. As a result, the beams do not vibrate in phase or with equal amplitudes so that the force and torque end reactions of beams do not cancel each other. Consequently, there is a loss of energy to the surrounding support structure and a subsequent reduction in the quality factor of the transducer.
There have been some attempts to modify transducer beams so that both beams resonate at the same frequency by placing trim masses on the beams in an effort to reduce the frequency differences and cause an increase in the overall quality factor of the transducer. In practice, trim masses are often made part of each beam by initially placing a base mass on each of the beams as part of the manufacturing process. The base masses are then selectively trimmed off one or both of the beams to form the trim masses, until testing indicates that both beams vibrate at the same frequency as indicated by an improved quality factor for the transducer. However, there are several limitations associated with adding trim masses to reduce the effects of the differences in the resonant frequencies of the beams. In many instances, the asymmetries between the beams only become apparent after the transducer is mounted to the device with which it is to be used. Selective trimming of the masses on the transducer, after it has been mounted is often very difficult, if not impossible, because the position of the transducer in the device makes it very impractical to selectively pare away portions of the masses by laser cutting or any other means.
Moreover, for many beam transducers used for force measurement, adding trim masses does not completely eliminate the resonant frequency differences and amplitude differences between the beams. This is because the trim masses can only be added to the beams to adjust for frequency differences between the beams forming the transducer at one specific resonant frequency. The resonant frequencies of the individual beams forming the transducer change as strain is applied to the transducer. Thus, when force is applied to a transducer during the transducer sensing process, when it is most desirable to maintain the high quality factor of the transducer, trim masses are not completely effective for equalizing the inherent resonant frequencies and amplitudes of the beams so that the quality factor of the transducer does not appreciably degrade.